Is it acceptable to use Cronbach's alpha to assess reliability of questionnaire composed of categorical and conditional items? Background: I have data on a questionnaire made up of categorical factual items. Some of them are binary and others have more than two categories.
For example:
1. Can you do painting (Yes- 1 point, No- 0 Point)
2. Do you have qualification in painting 
   (No - 0 point; Bachelor - 1 point; Postgraduate - 2 points)
3. Is there any painter(s) in your family (Yes- 1 point, No- 0 Point)     
Etc.

The questionnaire also contains conditional items. E.g., if someone chooses "No" for question 1, he or she will skip question 2 and jump to question 3. 
Question
Can I use Cronbach's alpha on a survey that contains categorical factual items?
I assume questions like these cannot be measured with Cronbach's Alpha.
I can't seem to find anyone using cronbach's alpha for such questionnaire. 
 A: Some quick rules


*

*If you have  unordered categorical data (i.e., three or more unordered categories; which you do), then you don't use Cronbach's alpha.

*If you have binary data (e.g., incorrect/correct data), then many people do use Cronbach's alpha, but see the Sjitsma reference given by @Momo.

*If you have conditional data, then that would at the very least complicate the application of Cronbach's alpha. Skip patterns often imply the existence of an implicit additional category (e.g., "Do you play soccer?" if yes, "what day of the week do you play most often?", you could say that for the second question, there is an implicit category of "not applicable") . However, in your example, skipping item 2 means that the person does not have a degree in painting. So you could fill in that information. In all these examples there are more than 2 unordered categories so you would not apply cronbach's alpha.


Other thoughts


*

*Cronbach's alpha relies on internal consistency to evaluate reliability. However, if your scale is formative, then internal consistency measures don't make much sense. In your case, I think your scale could be conceptualised as formative rather than reflective. I.e., the items in their totality represent something like "painting experience".

*You might want to look at something like test-retest correlation or categorical PCA if you need to calculate some form of reliability.

A: Generally Cronbach's coefficient $\alpha$ should not be used if you want a measure of reliability or internal consistency (which is what you need it for, I presume). See the OA Psychometrika article by Sjitsma. 
An easily available alternative is the GLB statistic (e.g. in R psych::glb).
Edit
Based on the comments by @chl I think the following caveat is in order: The "conditional questionnaire" structure will likely introduce blocks of missing values. I suppose the skip pattern and the missing value patterns induced will affect the (co-)variance estimation usually used in reliability coefficients if the missing value mechanism is not missing completely at random. Unfortunately, I don't know how this effect will look like though.  
A: If you are looking at Yes/No items or items coded of 0's and 1's, I have used Guttman's split Lambda 4 coefficient, which can be done in SPSS easily.
